Answer: [tex]v=\frac{2}{25}[/tex]
Step-by-step explanation:
To solve from v from the equation given in the problem you must apply the folowing proccedure:
- Add like terms:
[tex]-1+\frac{4}{3}=\frac{7}{2}v+\frac{2}{3}v\\\\ \frac{1}{3}=\frac{25}{6}v[/tex]
- Mulitply bot sides of thee equation by 6 and then divide both sids by 25.
Therefore you obtain:
[tex]\frac{1}{3}=\frac{25}{6}v\\\frac{6}{3}=25v\\v=\frac{2}{25}[/tex]
Answer:
v = 2/25
Step-by-step explanation:
We have given the equation:
-(2/3)v-1=(7/2)v-(4/3)
We have to solve it for v.
-(2/3)v-1=(7/2)v-(4/3)
(7/2)v+(2/3)v = -1+(4/3)
Multiply both sides of equation by 6 we get,
21v+4v = -6+8
25v = +2
Multiplying both sides by 1/25 we get,
v = 2/25
v = 2/25 is the answer.
two sides of a right triangle Measure 11 in and 15 in.
Part A
Use decimals rounded to the nearest tenth to complete the following statement. The length of the third side of the triangle could be ________ inches or ________ inches.
Part B
Write two side of the equations that justify your answers to Part A.
The sides could be 10.2 inches or 15.7 inches.
See the attached picture for the equations:
Phil had 93 dollars, and his sister had 10 dollars. How much should Phil give to his sister for each of them to have the same amount?
Answer:
$41.50
Step-by-step explanation:
He would have to give her $41.50 in order for them to have an equal amount of money, which would be $51.50.
Answer:
He should give her $41.50
Step-by-step explanation:
A rectangular price tag has an area of 36 square centimeters. Its perimeter is 26 centimeters. What are the dimensions of the price tag?
Final answer:
The dimensions of the price tag are 9 cm by 4 cm, which are found by solving two equations derived from the given area and perimeter.
Explanation:
The student is asking for the dimensions of a rectangular price tag that has an area of 36 square centimeters and a perimeter of 26 centimeters. To solve this, we need to use two formulas: one for area (A = length × width) and one for perimeter (P = 2 × (length + width)).
First, let's denote the length of the rectangle by l and the width by w. The given area, 36 cm2, implies that l × w = 36.
Second, we know the perimeter is 26 cm, which gives us the equation 2 × (l + w) = 26. Dividing both sides by 2, we get l + w = 13.
This system of equations can be solved using substitution or elimination. If we rearrange the perimeter equation to express one variable in terms of the other (for instance, w = 13 - l), we can then substitute this expression into the area equation. Solving for l and w afterwards will give us the required dimensions.
Through solving, we find that the dimensions of the rectangle are 9 cm by 4 cm, since 9 × 4 = 36 and 2(9 + 4) = 26.
Five friends share 3 bags of trail mix equally. What fraction of a bag of trail mix does each friend get? Please explain or show your work! :)
Each friend should get 1/5 of a bag of trail mix. Since there are three bags of trail mix, you would add those into it. Hope this helps!
In a sofa store 30% of the sofas are leather. 40% of the leather sofas are black. What percentage of the total number of sofas are made form black leather?
Answer:
12%
Step-by-step explanation:
Given,
% of leather sofas = p(A) = 30% = 30/100 = 0.3
% of leather sofas that are black = p(B) = 40% = 40/100 = 0.4
The percentage of total sofas made from leather = p(A) * p(B)
= 0.3 * 0.4
= .12
= 12%
The length of a rectangular park is 3 feet shorter than times its width. If the length is 123 feet, what is the width of the park in feet?
The width of the rectangular park is 126 feet. This was found by setting up an equation based on the problem description and then solving for the width.
Explanation:The subject of this question is Mathematics, specifically algebra. The problem states that the length of a rectangular park is 3 feet shorter than its width, with the length being given as 123 feet.
First of all, let's define the length with a variable L and the width with a variable W. From the problem, we can write the equation, L = W - 3. Since we know that L = 123 feet, we can substitute this value into the equation, getting 123 = W - 3.
To find W, all we need to do is add 3 to both sides of the equation. Hence, W = 123 + 3 = 126 feet. So, the width of the park is 126 feet.
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to the nearest thousandth what is the cosine of the angle formed by the line whose equation is y=2x and the positive x axis
The cosine of the angle formed by the line whose equation is y=2x and the positive x axis cos =63.435 to the nearest thousandth
What is meant by angle?When two straight lines or rays intersect at a common endpoint, an angle is formed. An angle's vertex is the common point of contact. The term angle is derived from the Latin word angulus, which means "corner." An angle is the difference in direction between two lines or surfaces. Angles are expressed in degrees.From a common point, the two hands draw different sets of lines. Angle refers to these groups of lines that originate from a common point. Every minute, the two hands form different angles. In real life, an example of an angle is a clock.To learn more about angle, refer to:
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Final answer:
To find the cosine of the angle formed by the line y=2x and the positive x-axis, we calculate the arctangent of the slope (2), which gives us an angle of approximately 63.435 degrees. The cosine of this angle is then approximately 0.447 to the nearest thousandth.
Explanation:
The question is asking for the cosine of the angle formed between the line y = 2x and the positive x-axis. To find this, we first need to determine the angle that the line makes with the x-axis. The slope of the line, given by m, is 2, which also represents the tangent of the angle the line forms with the x-axis (tan(θ) = m). We can calculate the angle using the arctangent function (tan⁻¹).
θ = tan⁻¹(2) = Approx. 63.435 degrees
The cosine of this angle can be found using the cosine function:
cos(θ) = cos(63.435 degrees) = Approx. 0.447
To the nearest thousandth, the cosine of the angle is 0.447.
A group of friends go to a local fair. Jason spends $3.75. My has spent three times as much as Jason. Tia spend $5.25 more than Maya how much money how much does Tia spend.
Answer:
$16.50
Step-by-step explanation:
If Jason spends $3.75 and Maya spends three times that amount, Maya spends 3.75(3) or $11.25. If Tia spends $5.25 more than Maya, Tia spends 11.25 + 5.25 or $16.50.
You got a job selling books at the mall. You are paid $70 per day plus $2 for each book you sell. Which recursive formula models this situation?
Answer:
f(x) = 70 + 2x
Step-by-step explanation:
In this problem, we first need to consider how much we get per day.
$70 is our constant.
$2 will be dependent on the number of books sold.
Here 'x' will represent the number of books sold.
f(x) = 70 + 2x
Now let's try it out.
Let's say we sold 0 books
f(0) = 70 + 2(0) = 70
This shows us that we only get our constant pay.
Now let's try for 1 or more books.
f(1) = 70 + 2(1) = 72
f(2) = 70 + 2(2) = 74
So the recursive formula f(x) = 70 + 2x is a good formula to model the situation.
Answer:
a1 = 70
an = an–1 + 2
Step-by-step explanation:
solve on the interval [0,2pi]
3sec x -2 = 1
Answer:
Final answer is [tex]x=0[/tex] and [tex]x=2\pi[/tex].
Step-by-step explanation:
Given equation is [tex]3\cdot\sec\left(x\right)-2=1[/tex]
Now we need to find the solution of [tex]3\cdot\sec\left(x\right)-2=1[/tex] in given interval [tex][0, 2\pi ][/tex].
[tex]3\cdot\sec\left(x\right)-2=1[/tex]
[tex]3\cdot\sec\left(x\right)=1+2[/tex]
[tex]3\cdot\sec\left(x\right)=3[/tex]
[tex]\frac{3\cdot\sec\left(x\right)}{3}=\frac{3}{3}[/tex]
[tex]\sec\left(x\right)=1[/tex]
which gives [tex]x=0[/tex] and [tex]x=2\pi[/tex] in the given interval.
Hence final answer is [tex]x=0[/tex] and [tex]x=2\pi[/tex].
Answer:
x = 0 and x = 2π
Step-by-step explanation:
We have given the equation.
3sec x -2 = 1
We have to solve it interval [0,2pi].
3sec x -2 = 1
3secx = 1+2
3secx = 3
secx = 1
x= sec⁻¹(1)
x = 0 and x = 2π is the answer in this interval.
Suppose f is a continuous function defined on a closed interval a,
b. (a) what theorem guarantees the existence of an absolute max- imum value and an absolute minimum value for f ? (b) what steps would you take to find those maximum and minimum values?
Answer:
Step-by-step explanation:
(a) The Extreme Value Theorem.
(b) We would differentiate the function and equate this to zero. The zeroes of the function will give us the values of the maxima / minima and we can find find the absolute maxima/minima from the results. Note we might have multiple relative maxima/ minima but only one absolute maximum and one absolute minimum.
Final answer:
The Extreme Value Theorem guarantees that a continuous function on a closed interval has an absolute maximum and minimum. To find these, one calculates the derivative to find critical points, analyzes the derivative's sign around these points, and evaluates the function at the critical points and the interval's endpoints.
Explanation:
Extreme Value Theorem and Finding Maximum and Minimum Values
The theorem that guarantees the existence of both an absolute maximum and minimum value for a continuous function defined on a closed interval a, b is known as the Extreme Value Theorem. This theorem plays a crucial role in calculus and mathematical analysis and is fundamental in understanding the behavior of continuous functions on closed intervals.
To find these maximum and minimum values, one would typically follow these steps:
Calculate f'(x), the derivative of the function f(x), to find the critical points.
Analyze the sign of f'(x) around the critical points to determine if they are local minima, local maxima, or saddle points.
Evaluate the function f(x) at each critical point as well as the endpoints of the interval [a, b] to determine the absolute extrema.
Moreover, if a function satisfies the criteria of being continuous on [a, b] and differentiable on (a, b), then by a related theorem called the Mean Value Theorem, there exists at least one c in (a, b) where f'(c) = 0.
These methods form the standard procedure for finding the extremal values that a continuous function may possess on a closed interval.
An arc is intercepted by a central angle of 3π2 radians on a circle with a radius of 18 centimeters. What is the exact length of the arc? Enter your answer, in terms of π , in the box.
Answer:
The length of the arc is [tex]27\pi \ cm[/tex]
Step-by-step explanation:
step 1
Find the circumference
we know that
The length of a complete circle is equal to the circumference of the circle
The circumference is equal to
[tex]C=2\pi r[/tex]
we have
[tex]r=18\ cm[/tex]
substitute
[tex]C=2\pi (18)[/tex]
[tex]C=36\pi\ cm[/tex]
step 2
we know that
A central angle of [tex]2\pi[/tex] radians subtends the circumference of [tex]36\pi\ cm[/tex]
so
by proportion
Find the length of the arc by a central angle of [tex]\frac{3\pi }{2}[/tex] radians
[tex]\frac{36\pi }{2\pi}\frac{cm}{radians}=\frac{x}{(3\pi/2)}\frac{cm}{radians} \\ \\x=18*(3\pi/2)\\ \\x=27\pi \ cm[/tex]
The lengths of plate glass parts are measured to the nearest tenth of a millimeter. The lengths are uniformly distributed with values at every tenth of a millimeter starting at 590.1, and continuing through 590.8. Determine the mean and variance of the lengths. (a) mean (in tenths of millimeters) Round your answer to two decimal places (e.g. 98.76). (b) variance (in tenths of millimeters2) Round your answer to three decimal places (e.g. 98.765). (a)
Answer:
A) μ = 590.45 mm; B) σ² = 0.053 mm
Step-by-step explanation:
To find the mean, we add together all of the values and divide by the number of data values:
590.1+590.2+590.3+590.4+590.5+590.6+590.7+590.8 = 4723.6
There are 8 data values; this gives us
4723.6/8 = 590.45
To find the variance, we subtract each of the data values from the mean. We then square this difference, and find the mean of the squares:
590.1-590.45 = -0.35; (-0.35)² = 0.1225
590.2-590.45 = -0.25; (-0.25)² = 0.0625
590.3-590.45 = -0.15; (-0.15)² = 0.0225
590.4-590.45 = -0.05; (-0.05)² = 0.0025
590.5-590.45 = 0.05; (0.05)² = 0.0025
590.6-590.45 = 0.15; (0.15)² = 0.0225
590.7-590.45 = 0.25; (0.25)² = 0.0625
590.8-590.45 = 0.35; (0.35)² = 0.1225
(0.1225+0.0625+0.0225+0.0025+0.0025+0.0225+0.0625+0.1225)/8
= 0.42/8 = 0.0525 ≈ 0.053
(a) The mean of the glass parts rounded to nearest tenths of millimeters
= 590.45 and (b) Variance in tenths of millimeters is = 0.053 mm.
What is mode ?In a given set of data one which repeats most frequently is called the mode of the given data set.
To obtain the mean we add together all of the values and divide by the number of data values.
590.1+590.2+590.3+590.4+590.5+590.6+590.7+590.8 = 4723.6
There are 8 data values; this gives us
4723.6/8 = 590.45
To find the variance, we subtract each of the data values from the mean and we square this difference to find the mean of the squares.
590.1-590.45 = -0.35; (-0.35)² = 0.1225
590.2-590.45 = -0.25; (-0.25)² = 0.0625
590.3-590.45 = -0.15; (-0.15)² = 0.0225
590.4-590.45 = -0.05; (-0.05)² = 0.0025
590.5-590.45 = 0.05; (0.05)² = 0.0025
590.6-590.45 = 0.15; (0.15)² = 0.0225
590.7-590.45 = 0.25; (0.25)² = 0.0625
590.8-590.45 = 0.35; (0.35)² = 0.1225
(0.1225+0.0625+0.0225+0.0025+0.0025+0.0225+0.0625+0.1225)/8
= 0.42/8 = 0.0525 and rounded to tenths of millimeters is 0.053
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The complement of an angle is one-sixth the measure of the supplement of the angle. What is the measure of the complement angle?
Answer:
The measure of the complement angle is [tex]18\°[/tex]
Step-by-step explanation:
Let
x-----> the angle
we know that
The complement of an angle is equal to [tex](90-x)\°[/tex]
The supplement of an angle is equal to [tex](180-x)\°[/tex]
we have
The complement of an angle is one-sixth the measure of the supplement of the angle
[tex](90-x)\°=(1/6)(180-x)\°[/tex]
solve for x
[tex](540-6x)\°=(180-x)\°[/tex]
[tex](6x-x)=(540-180)\°[/tex]
[tex](5x)=(360)\°[/tex]
[tex]x=72\°[/tex]
Find the measure of the complement angle
[tex](90-x)\°[/tex] ------> [tex](90-72)=18\°[/tex]
Answer:
18⁰
Step-by-step explanation:
Angle = x
Complement = 90 - x
Supplement = 180 - x
Given:
90 - x = 1/6 × (180 - x)
540 - 6x = 180 - x
5x = 360
x = 72
Complement = 90 - 72 = 18⁰
Help which expression represents the phrase 8 less than the product of 6 and a number x
Answer:
8 < 6x
Step-by-step explanation:
Just write what you see by the letters
The length of a rectangle is four times its width. If the area of the rectangle is 100 ft?, find its perimeter
The width of the rectangle is 5 feet, its length is 20 feet. Thus, the perimeter is 50 feet.
To solve this problem, let's denote:
- Width of the rectangle as w (in feet)
- Length of the rectangle as 4w (since it's four times the width)
Given that the area of the rectangle is 100 square feet, we can set up the equation for the area:
[tex]\[ \text{Area} = \text{Length} \times \text{Width} \][/tex]
[tex]\[ 100 = (4w) \times w \][/tex]
[tex]\[ 100 = 4w^2 \][/tex]
Now, let's solve for ( w ):
[tex]\[ 4w^2 = 100 \][/tex]
Divide both sides by 4:
[tex]\[ w^2 = 25 \][/tex]
Taking the square root of both sides:
[tex]\[ w = \sqrt{25} \][/tex]
[ w = 5 ]
So, the width of the rectangle is ( w = 5 ) feet.
Now, we can find the length:
[tex]\[ \text{Length} = 4w = 4(5) = 20 \] feet.[/tex]
Now that we have both the width and length, we can find the perimeter of the rectangle using the formula for perimeter:
[tex]\[ \text{Perimeter} = 2(\text{Length}) + 2(\text{Width}) \][/tex]
[tex]\[ \text{Perimeter} = 2(20) + 2(5) \][/tex]
[tex]\[ \text{Perimeter} = 40 + 10 \][/tex]
[tex]\[ \text{Perimeter} = 50 \][/tex]
So, the perimeter of the rectangle is ( 50 ) feet.
Bernie wants to write equations in the form y=mx+b for the lines passing through point P that are parallel and perpendicular to line r. First he finds the slopes of these two lines. What could he do next to find the y-intercepts?
Answer:
Substitute the slope and the coordinates of point P in the equation of the line y=mx+b and then solve for b in each equation
Step-by-step explanation:
we know that
The first step is calculate the slopes of these two lines. Remember that if two lines are parallel then the slopes are the same (m1=m2) and if two lines are perpendicular then the slopes is equal to m1*m2=-1
The second step is substitute the slope m2 and the coordinates of point P in the equation of the line in slope-intercept form y=mx+b and then solve for b in each equation
Answer:
Step-by-step explanation: See answer below
40 packs of baseball cards for discounted price of 64 he sells 30 packs of baseball cards to A friend at cost much should he charge
PLEASE HELP!! TIMED QUESTION!!!!!
If f(x) = x^2 + 3x + 5 , what is f (a + h) ?
A. (a+h)^2 + 3(a+h) + 5(a+h)
B. a^2 + 2ah + h^2 + 3a + 3h + 5
C. h^2 + 3a + 3h + 5
D. (x^2 + 3ax + 5) (a + h)
Answer:
[tex]\large\boxed{B.\ a^2+2ah+h^2+3a+3h+5}[/tex]
Step-by-step explanation:
[tex]f(x)=x^2+3x+5\\\\f(a+h)\to\text{substitute}\ x=a+h\ \text{to the equation:}\\\\f(a+h)=(a+h)^2+3(a+h)+5\\\\\text{Use}\ (x+y)^2=x^2+2xy+y^2\ \text{and the distributive property}\\\\f(a+h)=a^2+2ah+h^2+3a+3h+5[/tex]
What percentage of the data values falls between the values of 3 and 24 in the data set shown?
What percentage of the data values falls between the values of 3 and 24 in the data set shown?
25%
50%
75%
100%
25%
50%
75%
100%
Answer: 100%
Step-by-step explanation:
We are given a Box- plot, in which the minimum value is described by the left whisker is 3 and the maximum value is described by the right whisker is 24.
Since the range of all data values in a data is given from minimum value to the maximum value.
⇒ The percentage of the data values falls between the values of 3 and 24 in the data set shown = 100%
When b= 0.5, the period of orange graph is _ pi
When b= 2, the period of orange graph is _ pi
Answer:
When b= 0.5, the period of orange graph is _4_ pi
When b= 2, the period of orange graph is _1_pi
Step-by-step explanation:
The period of the sinusoidal functions can be easily calculated by observing their graphs.
First, look at the orange graph when b = 0.5
Identify a point where the orange chart cuts the x-axis. For example at [tex]x = 0[/tex]. After completing the rise and fall cycle, the function cuts back to the x axis at [tex]x = 4\pi[/tex].
Then the period [tex]T = 4\pi[/tex].
Second, look at the orange graph when b = 2
Identify a point where the orange chart cuts the x-axis. For example at [tex]x = 0[/tex]. After completing the rise and fall cycle, the function cuts back to the x-axis at [tex]x = \pi[/tex].
Then the period [tex]T = \pi[/tex].
We also know that the period of a sinusoidal function is defined as [tex]T(b) = \frac{2\pi}{b}[/tex]
So:
[tex]T(0.5) = \frac{2\pi}{0.5} = 4\pi\\\\T(2) = \frac{2\pi}{2} = \pi[/tex]
Answer:
Part 2:
Based on this evidence,
When b > 1, the period
✔ decreases
.
When 0 < b < 1, the period
✔ increases
Step-by-step explanation:
This is correct for edge 2020. Hope this helps someone.
What is the value of x? Enter your answer in the box.
Check the picture below.
notice, we use the 30-60-90 rule to get the length of RT, and then the 45-45-90 rule to get "x".
Answer:
Step-by-step explanation:
Remark
x is going to be the same thing as the hypotenuse of ΔRST. Find that and you have x.
Givens
<STR = 60°
RT = 2√3
Solution
Sin(60°) = opposite / hypotenuse
Sin(60°) = √3 / 2
Sin (60°)= 2 √3 / hypotenuse
hypotenuse = 2√3 // sin(60°)
hypoteneuse = 2√3 /√3/2
[tex]\text{hypotenuse = }\dfrac{2\sqrt{3}}{\dfrac{\sqrt{3} }{2}} = 2*2[/tex]
The √3's cancel. The answer is 4
========================
ΔRTQ is a right angle isosceles triangle
∴RT = RQ
X = 4
Maggie buys 4 shirts that are the same but in different colors.The total cost for all 4 shirts before sale tax is 85.80 if all 4 shirts the same price how much does 1 cost
Jessie's daughter went to Target and bought $1 or $2 items from the One Spot area. She wants to spend less than $20 at Target
She can buy 20 1$ items, or 10 $2 items, at most
The scale on a map is 5 cm : 8 km. If the distance between two cities is 56 km, how far apart in cm are the two cities on the map
Answer: 250km
Step-by-step explanation:
Answer:
The cities are 35 cm apart in map.
Step-by-step explanation:
The scale on a map is 5 cm : 8 km.
[tex]\texttt{Scale = }\frac{5cm}{8km}\\\\\texttt{Scale = }\frac{5cm}{8\times 100000cm}=\frac{5}{800000}[/tex]
Now we need to find how much is the distance in map if the original distance is 56 km.
Distance in map = Scale x Original distance
[tex]\texttt{Distance in map = }\frac{5}{800000}\times 56km=\frac{5\times 5600000cm}{800000}=35cm[/tex]
The cities are 35 cm apart in map.
Determine whether the given equation has one solution, no solution, or infinitely many solutions: 4x+10=2(2x+5)
if we distribute 2(2x+5), we'll end up with 4x + 10, so in short, the right-hand-side, is really the left-hand-side in disguise.
and since 4x + 10 = 4x + 10, both equations are equal, meaning in short, the system has an infinite number of solutions.
Use trigonometric identities to rewrite the equation sec0/csc0=1 (picture provided)
Answer: option b.
Step-by-step explanation:
To solve this exercise you must keep on mind the identities shown below:
1) [tex]sec\theta=\frac{1}{cos\theta}[/tex]
2) [tex]csc\theta=\frac{1}{sin\theta}[/tex]
3) [tex]tan\theta=\frac{sin\theta}{cos\theta}[/tex]
Therefore, to rewrite [tex]\frac{sec\theta}{csc\theta}=1[/tex] you must substitute identities and simplify the expression, as following:
[tex]\frac{sec\theta}{csc\theta}=1\\\\\frac{\frac{1}{cos\theta}}{\frac{1}{sin\theta}}=1\\\\\frac{sin\theta}{cos\theta}=1\\\\tan\theta=1[/tex]
Therefore, as you can see, the answer is the option b.
Answer:
Step-by-step explanation: B
The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 5 to 8. If there were 3585 yes votes, what was the total number of votes?
Answer: 9321 votes
Step-by-step explanation:
1- You can express the ratio as following:
[tex]5:8[/tex] or [tex]\frac{5}{8}[/tex]
2- Let's call the number of no votes "N"
3- Therefore, if there were 3585 yes votes, then you can write the following expression to calculate the number of no votes:
[tex]\frac{5}{8}=\frac{3585}{N}\\\\N=\frac{3585*8}{5}\\\\N=5736[/tex]
4- Then, the total number of votes is:
[tex]t=3585votes+5736votes=9321votes[/tex]
Answer:
9321
Step-by-step explanation:
We can simply make a ratio (fraction) to solve this. Let total number of NO votes be N. Shown below is the ratio:
[tex]\frac{YesVotes}{NoVotes}=\frac{5}{8}=\frac{3585}{N}[/tex]
Now we can cross multiply and solve for N:
[tex]\frac{5}{8}=\frac{3585}{N}\\5N=8*3585\\5N=28,680\\N=\frac{28680}{5}=5736[/tex]
Hence, number of NO votes is 5736.
To get TOTAL number of votes, we add number of yes votes (3585) to that of number of no votes (5736).
Total votes = 3585 + 5736 = 9321
1. Find the missing side length. Round your answer to the nearest tenth.
6.7 21.3 5.5 43.2
2. Find the length of side a. Round to the nearest tenth.
12 378.4 18.3 19.5
3. Find the length of side BA. Round to the nearest hundredth.
0.42 0.65 0.83 1.25
QUESTION 1
We can use the cosine rule to find the missing side length.
Recall that the cosine rule for a triangle with sides a,b,c and an included angle A is
[tex]a^2=b^2+c^2-2bc\cos A[/tex]
Let the missing side length in the triangle with sides 6, 9 and the included angle of [tex]37\degree[/tex] be [tex]a[/tex] units.
We then substitute the values into the cosine rule to obtain;
[tex]a^2=6^2+9^2-2(6)(9)\cos 37\degree[/tex]
[tex]a^2=36+81-108\cos 37\degree[/tex]
[tex]a^2=30.747[/tex]
[tex]\Rightarrow a=\sqrt{30.747}[/tex]
[tex]\Rightarrow a=\sqrt{30.747}[/tex]
[tex]\Rightarrow a=5.5[/tex] units to the nearest tenth.
QUESTION 2
We again use the cosine rule: [tex]a^2=b^2+c^2-2bc\cos A[/tex]
We substitute the given values to obtain;
[tex]a^2=11^2+13^2-2(11)(13)\cos 108\degree[/tex]
[tex]a^2=121+169-286\cos 108\degree[/tex]
[tex]a^2=378.379[/tex]
[tex]\Rightarrow a=\sqrt{378.379}[/tex]
[tex]\Rightarrow a=19.5[/tex] to the nearest tenth
QUESTION 3
We again use the cosine rule :
[tex]|BA|^2=(\frac{1}{2})^2+(\frac{1}{3})^2-2(\frac{1}{2})(\frac{1}{3})\cos 100\degree[/tex]
[tex]|BA|^2=0.418899[/tex]
[tex]|BA|=\sqrt{0.418899}[/tex]
[tex]|BA|=0.65[/tex] to the nearest hundredth
If a point a is located at 2/3 and there are 10 points between A and B what could be the possible coordinates for point B
The possible coordinates for point B that are 10 units away from point A at (2,-3) could be (12, -3), (2, 7), (-8, -3), or (2, -13), moving directly horizontal or vertical.
If point A is located at (2,-3), and there are 10 points between A and B, we're likely looking at points equidistant from A, forming a sort of 'circle' with A at the centre. However, in a Cartesian plane, if the distance between two points is equal to 10 units, there are various possibilities depending on the orientation of the line connecting the two points.
For a point B to be 10 units away from point A at (2, -3), it can move horizontally to the right or left, or vertically up or down. Thus, the possible coordinates for point B would change by 10 units either in the x-coordinate (horizontally) or the y-coordinate (vertically).
Possible Coordinates for Point B
Horizontally to the right: (2+10, -3) = (12, -3)
Vertically up: (2, -3+10) = (2, 7)
Horizontally to the left: (2-10, -3) = (-8, -3)
Vertically down: (2, -3-10) = (2, -13)
Other options like (12, -6), (2, -7), (12, 3), or (-8, 3) do not adhere to being 10 units away from point A directly horizontally or vertically.
The complete question is:
If point A is located at (2,-3) , and there are 10 points between A and B, what * 1 could be the possible coordinates for point B? Choose all that apply. (12,-3) (2,7) (12,-6) (-8,-3) (2,-7) (-8,3) (2,-13) (12,3)